Distribution of roundoff noise in binary floating-point addition
K. Kalliojärvi, Yrjo A. Neuvo · 2003
A method for deriving the distribution of relative round off error in addition of two binary floating-point numbers is introduced. The distribution is needed in the calculation of variance of the relative roundoff error in floating-point addition. The resulting distribution depends on the statistics of the addends and the rounding strategy chosen. As an example, the distribution is derived for the addition of two uncorrelated numbers from Gaussian distribution. The result was verified by simulation.>